OFFSET
1,2
LINKS
Eric Weisstein's World of Mathematics, Independence Number
Eric Weisstein's World of Mathematics, Knight Graph
EXAMPLE
1;
2, 4;
3, 4, 5;
4, 4, 6, 8;
5, 6, 8, 10, 13;
6, 8, 9, 12, 15, 18;
MATHEMATICA
Table[IndependenceNumber[KnightTourGraph[m, n]], {n, 10}, {m, n}] // Flatten
Table[Piecewise[{{Max[m, n], Min[m, n] == 1}, {Max[m, n] + 1, Min[m, n] == 2 && Mod[Max[m, n], 2] == 1}, {4 Round[(Max[m, n] + 1)/4], Min[m, n] == 2 && Mod[Max[m, n], 2] == 0}, {m n/2, Mod[m n, 2] == 0}, {(m n + 1)/2, Mod[m n, 2] == 1}}], {n, 10}, {m, n}] // Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Eric W. Weisstein, Jun 01 2017
STATUS
approved